Question

Rewrite the expression without using a negative exponent.

Simplify your answer as much as possible.

Answer 1

To rewrite an expression without a negative exponent, take the reciprocal of the base with the positive exponent. Division of exponentials requires dividing coefficients and subtracting exponents of the same base. Eliminate negative exponents and simplify the expression to get the final result.

Step-by-step explanation:

To rewrite an expression without a negative exponent, you simply take the reciprocal of the base and use the positive exponent. For example, seeking to rewrite x-n, you would transform it into 1/xn, moving the base x to the denominator and making the exponent positive.

Division of exponentials involves simplifying expressions by dividing the coefficients and subtracting exponents when the bases are the same. For instance, for expressions like am / an, the result would be am-n. In case there are numerical coefficients in front, divide those numbers directly. After simplifying, always check whether the answer makes sense and is in the simplest form.

Working with negative exponents, it's crucial to eliminate terms that result in a more straightforward expression and confirm that no negative exponents remain in the final answer, ensuring it is in its acceptable form.

Answer 2

`(n^4)/(4)`

or

`(1)/(4) n^4`

Step-by-step explanation:

The given expression is

`(1)/(4n^(-4))`

This is an exponential expression with a negative index in the denominator.

We can rewrite the expression so that it will be,

`=(1)/(4)* (1)/(n^(-4))`

We now apply this property of indices. A negative index in the denominator becomes a positive index in the numerator.

`(1)/(a^(-m)) =a^(m)`

When we apply this we get,

`=(1)/(4)* n^(4)`

We then simplify to obtain,

`=(1)/(4)n^(4)`